Question

If cosec θ = 5/3, then what is the value of cos θ + tanθ​

Answer 1

Answer :

cosθ + tanθ = 31/20

Solution :

• Given : cosecθ = 5/3
• To find : cosθ + tanθ = ?

We have ,

cosecθ = 5/3

Also ,

We know that ,

cosecθ = h/p

Thus ,

cosecθ = h/p = 5/3

Here ,

h = 5

p = 3

Now ,

As per Pythagoras theorem , we have ;

=> p² + b² = h²

=> 3² + b² = 5²

=> 9 + b² = 25

=> b² = 25 - 9

=> b² = 16

=> b = √16

=> b = 4

Now ,

=> cosθ = b/h

=> cosθ = 4/5

Also ,

=> tanθ = p/b

=> tanθ = 3/4

Now ,

=> cosθ + tanθ = 4/5 + 3/4

=> cosθ + tanθ = (16 + 15)/20

=> cosθ + tanθ = 31/20

Hence ,

cosθ + tanθ = 31/20

Answer 2

Answer:

$\huge \mathfrak {given}$

• cosecθ= 5/3

$\huge \mathfrak {to \: find}$

Value of cosθ + tanθ

$\huge \mathfrak {solution}$

As we know that,

$\sf \cos\sec( \theta) = \dfrac{h}{p}$

$\cos \sec( \theta ) = \dfrac{5}{3}$

Now,

We will apply Pythagoras theorem

$\tt {p}^{2} + {b}^{2} = {h}^{2}$

$\tt \: {3}^{2} + {b}^{2} = {5}^{2}$

$\tt \: 9 + {b}^{2} = 25$

$\tt \: {b}^{2} = 25 - 9$

$\tt {b}^{2} = 16$

$\tt \: b \: = \sqrt{} 16$

$\tt \: b \: = 4$

Now cos∅ = 4/5

$\huge \bf \: \cos( \theta) + \tan( \theta) =$

$\tt \: \dfrac{4}{5} + \dfrac{3}{4}$

$\ \tt \: \dfrac{16 + 15}{20}$

$\huge \boxed{ \sf cos( \theta \: ) + \tan( \theta \: ) = \frac{31}{20} }$